From the introduction: For fifty years econometric analyses of treatment response have made extensive use of instrumental variable (IV) assumptions holding that mean response is constant across specified subpopulations of a population of interest. Yet the credibility of mean independence conditions and other IV assumptions has often been a matter of considerable disagreement, with much debate about whether some covariate is or is not a “valid instrument” in an application of interest. There is therefore good reason to consider weaker but more credible assumptions. To this end, we introduce monotone instrumental variable (MIV) assumptions holding that mean response varies weakly monotonically across specified subpopulations. We study the identifying power of these MIV assumptions and give an empirical application. The findings reported here add to the literature developing nonparametric bounds on treatment effects.